Question

В треугольнике АВС угол С прямой, ВС=6, cos B=0,3. Найдите АВ. (Можно без чертежа)

Answer 1

Cos есть отношение прилежащего катета к гипотенузе; соs B=BC/AB, отсюда найдем AB; 0,3 = 6/AB; AB = 6/0,3= 20;

Answer 2

Problem Analysis

We are given a triangle ABC, where angle C is a right angle (C = 90 degrees), BC = 6, and cos(B) = 0.3. We need to find the length of AB.

Solution

To find the length of AB, we can use the cosine rule, which states that in a triangle with sides a, b, and c, and angle A opposite side a, the following equation holds:

c^2 = a^2 + b^2 - 2ab * cos(C)

In our case, we know that angle C is a right angle, so cos(C) = 0. Therefore, the equation simplifies to:

c^2 = a^2 + b^2

Substituting the given values, we have:

AB^2 = AC^2 + BC^2

Since angle C is a right angle, we can use the Pythagorean theorem to find the length of AC:

AC^2 = AB^2 + BC^2

Substituting the given values, we have:

AB^2 = AC^2 + BC^2 = AB^2 + 6^2

Simplifying the equation, we get:

AB^2 - AB^2 = 6^2

0 = 36

This equation is not possible, as it implies that AB is equal to 0, which is not valid for a triangle. Therefore, there is no solution to this problem.

Conclusion

In the given triangle ABC, where angle C is a right angle, BC = 6, and cos(B) = 0.3, it is not possible to determine the length of AB. The equation derived from the given information leads to an invalid solution.